infinities

Webster's Dictionary (GCIDE)

Infinity \In*fin"i*ty\, n.; pl. Infinities. [L. infinitas; pref. in- not + finis boundary, limit, end: cf. F. infinit['e]. See Finite.] [1913 Webster]

1.Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity. --Sir T. More. [1913 Webster]

There can not be more infinities than one; for one of them would limit the other.— Sir W. Raleigh.[1913 Webster]

2.Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections. --Hooker. [1913 Webster]

3.Endless or indefinite number; great multitude; as an infinity of beauties. --Broome. [1913 Webster]

4.(Math.) A quantity greater than any assignable quantity of the same kind. [1913 Webster]

Note: Mathematically considered, infinity is always a limit of a variable quantity, resulting from a particular supposition made upon the varying element which enters it. --Davies & Peck (Math. Dict.). [1913 Webster]

5.(Geom.) That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity. [1913 Webster]

Circle at infinity, an imaginary circle at infinity, through which, in geometry of three dimensions, every sphere is imagined to pass.

Circular points at infinity. See under Circular. [1913 Webster]